Optimal Taxation Of Capital Income In A Growth Model With ...

Worlung Paper 95 10

OPTIMAL TAXATION OF CAPITAL INCOME IN A GROWTH MODEL WITH MONOPOLY PROFITS

by Jang-Ting Guo and Kevin J. Lansing

Jang-Ting Guo is a professor of economics at the University of California, Riverside, and Kevin J. Lansing is an economist at the Federal Reserve Bank of Cleveland. For helpful comments, the authors thank Steven Cassou, Stephen Cecchetti, Roger Farmer, Finn Kydland, Randall Wright, seminar participants at the 1995 Western Economic Association meetings, and two anonymous referees.

Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment. The views stated herein are those of the authors and are not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System.

September 1995

clevelandfed.org/research/workpaper/1995/wp9510.pdf

ABSTRACT

This paper shows that the optimal steady-state tax on capital income in a neoclassical growth model can be positive, negative, or zero, depending crucially on the level of monopoly profits and the degree to which profits can be taxed. With an empirically plausible level of profits, the model implies that the optimal steady-state tax on capital can range between -6 percent and 24 percent, depending on the structure of dividend taxation. Similarly, we find that the available welfare gain of switching from the existing U.S. tax policy to a revenue-neutral optimal tax policy can range between 0.8 percent and 3.9 percent of steady-state output.


1. Introduction

An important issue for U.S. policymakers is whether capital gains should be taxed as ordinary

income (as they are now) or be given some form of tax-favored treatment. Judd (1985) and Chamley

(1986) show that, in the long run, the standard neoclassical growth model implies that capital income

should not be taxed at all, that is, the optimal steady-state tax on capital income is zero. Based on this

result, other researchers, such as Lucas (1990), Cooley and Hansen (1992), and McGrattan, Rogerson,

and Wright (1993) estimate that there exist large unexploited gains to eliminating the U.S. capital tax.

In this paper, we augment the standard model to allow for the possibility of monopoly profits

and show that the optimal steady-state tax on capital income can be positive, negative, or zero. The

optimal tax rate depends crucially on the level of monopoly profits and the degree to which profits can

be taxed. In particular, we adopt a model of the production environment developed by Benhabib and

Farmer (1994) in which producers of intermediate goods possess a degree of monopoly power that can

be characterized by a single parameter. The model embeds the perfect competition environment assumed

by Judd (1985) and Chamley (1986) as a special case.

The consideration of monopoly power introduces two competing effects that interact to determine

the optimal steady-state tax on capital income. First, households underinvest relative to the socially

optimal level because the interest rate that governs their investment decisions is less than the marginal

product of capital. This "underinvestment effect" represents the classic inefficiency of a monopoly, and

results in lower long-run levels of capital and output in comparison to the perfectly competitive case.

To correct this inefficiency, the government can subsidize capital accumulation (and stimulate output)

by imposing a negative tax rate on capital income.

The second effect derives from the fact that f m s with monopoly power earn pure economic

profits. Since profits do not affect household decisions at the margin, the government would like to tax

profits at a rate of 100 percent, thereby allowing other distortionary taxes to be reduced. When the tax

authority does not distinguish between profits and other types of capital income (as we assume), then

the capital tax can also function as a tax on profits, but one with an endogenous upper bound. We show

that the strength of this "profit effect" depends on the structure of dividend taxation. If profits are taxed

at both the firm level and the household level (in what is called a double-taxation-of-dividends policy),


then the capital tax collects a large fraction of revenue from profits. This strengthens the profit effect

and motivates the government to choose a higher capital tax for a given level of monopoly profits.

Our model allows for a rich set of possibilities regarding the optimal steady-state tax on capital

income. For example, if the profit effect is stronger than the underinvestment effect, then the optimal

tax rate is positive. This result complements recent research by Jones, Manuelli, and Rossi (1993),

Aiyagari (1 994), and ~rnrohoro~lu (1994), who provide alternative theoretical justifications for a positive

optimal tax rate on capital in the long run. If the profit effect exactly cancels the underinvestment effect,

then the optimal tax rate can be zero even in an economy without perfect competition. If profits can be

completely taxed away by some separate instrument (or if the firm's fixed costs imply zero profits), then

the underinvestment effect will still remain and the optimal tax rate is negative. The perfect competition

result obtained by Judd (1985) and Chamley (1986) represents a special case of our model, in which

neither of the two effects described above is present.

The ambiguity regarding the sign of the optimal long-run capital tax is directly analogous to the

findings of Stiglitz and Dasgupta (1971). They find that the optimal commodity tax policy for a

monopolistic industry with profits will generally include both differential taxes and subsidies. The link

between differential commodity taxation and the capital tax in our model is very direct; a positive

(negative) capital tax implies that future consumption goods are taxed at a higher (lower) rate than

present consumption goods.

Given the inconclusive nature of the theory, we undertake a quantitative assessment of the

optimal tax policy in a calibrated version of our model. When the profit-to-output ratio is 5 percent (a

typical value for U.S. manufacturing industries), we find that the optimal steady-state tax on capital

income can range between -6 percent and 24 percent, depending on the level of dividend taxation.

Similarly, we find that the available welfare gain of switching from the existing U.S. tax policy to a

revenue-neutral optimal tax policy can range between 0.8 percent and 3.9 percent of steady-state output.

Higher levels of dividend taxation imply lower welfare gains because revenue that was previously

obtained by a tax on profits must now be replaced with a higher distortionary tax on labor. Thus, our

results suggest that previous estimates regarding the benefits of reducing the U.S capital tax may be

overstated.


The remainder of this paper is organized as follows. Section 2 describes the model. In section

3, we derive the expressions that determine the optimal steady-state tax on capital income. Sections 4

and 5 discuss computation issues and the choice of parameter values. Section 6 presents our quantitative

results, and section 7 concludes.

2. The Model

The model economy consists of three types of agents: households, firms, and the government.

The production environment differs from the standard competitive framework used by Judd (1985) and

Chamley (1986). In particular, we allow for the possibility that intermediate goods producers possess

monopoly power. This implies that firms can realize positive economic profits even though the final-

goods sector of the economy is perfectly competitive. As owners of the firms, households receive net

profits in the form of dividends. Various options regarding the taxation of these dividends are

considered.

2.1 The Household's Problem

There is a large number of identical, infinitely lived households, each of which maximizes a

stream of discounted utilities over sequences of consumption and leisure:

The within-period utility function U ( -) is increasing in private consumption c, and decreasing

in hours worked h, . The parameter P is the constant discount factor. The function V( - ) is increasing

in g,, where g, represents per capita public consumption goods which are determined outside of

households' control. Both U ( .) and V( - ) are assumed to be continuously differentiable, bounded, and

concave. The additive separability in g, implies that public consumption does not affect the marginal

utility of private consumption, a specification supported by parameter estimates in McGrattan, Rogerson,

and Wright (1993). Although this specification is not necessary for our results, it simplifies the

computations because V( .) can be ignored when deriving the household optimization conditions.


The representative household faces the following within-period budget constraint:

C, + ~ , + b , + ~ I (l-~,,)w,h, + ( l - ~ ~ , ) ( r , k , + f i , + r ~ , b , ) + S Z ~ , ~ , +b,, ko, bo given, (2)

where x, is private investment, kt is private capital, and b,, represents one-period, real government bonds

canied into period t+l by the household. Households derive income by supplying labor and capital

services to firms at rental rates w, and r,. Two additional sources of household income are the firm's

net profits ft,, which are distributed to households as dividends, and the interest earned on government

bonds rb, b, .

We impose a restriction that prevents the government from taxing away monopoly profits. In

particular, we assume that the tax authority does not distinguish between profits and other types of

capital income. As a result, the tax on capital income also functions as a tax on profits, but one with an

endogenous upper bound. This scenario is reflected in equation (2), where net profits A,, capital rental

income r, kt, and bond interest rbt b, are all taxed at the same rate zk, . Labor income is taxed at the rate

z,, . The term ST, kt represents a depreciation allowance, where 6 is the constant depreciation rate.

Households view tax rates, wages, interest rates, and dividends as determined outside their control.

The following equation describes the law of motion for the capital stock:

The household first-order conditions with respect to the indicated variables and the associated

transversality conditions (TVC) are:


TVC: lim Pth,k,+, = 0, lim P I X , b,+, = 0, I+=- I +=-

where A, is the Lagrange multiplier associated with the budget constraint (2). The transversality

conditions ensure that (2) can be transformed into an infinite-horizon, present-value budget constraint.

2.2 Production Environment

Our description of the production environment closely follows the model developed by Benhabib

and Farmer (1994). There exists a continuum of intermediate goods y, , i E [O, I], and a unique final good

y, that is produced using the following constant-returns-to-scale technology:

Final-goods producers choose y, in order to maximize profits: y, - I,' pi, yiI di, where pi, is the

relative price of the i th intermediate good. Profit maximization implies pi, = (y, Iy,) X-l, which is the

demand function for intermediate goods. When x < 1, intermediate goods producers perceive a downward

sloping demand curve. In this case, the firm earns an economic profit that is distributed to households

in the form of dividends. When x = 1, however, intermediate goods are perfect substitutes in the

production of the final good, and the intermediate sector becomes perfectly competitive. The technology

for producing intermediate goods is given by

where kit and hi, are the capital and labor inputs of the ith firm. The decision problem of an


intermediate-goods producer can be summarized as

subject to: p i = ( y I y , yi, = kir hi:-'.

In (7), we allow for the possibility that the firm's profits may be taxed directly. The

government's use of the tax rate T,, for this purpose implies that the tax authority does not distinguish

between households and firms when assessing taxes on capital income. As before, this ensures that

profits will not be completely taxed away. When y= 2, profits are initially taxed at the firm level and

then taxed again as dividends at the household level. We refer to this case as a double taxation of

dividends policy. When y= 1, dividends are taxed only at household level. When y= 0, the effective

tax rate on dividends is zero. In reduced form, the y = 0 case can be viewed as capturing the possibility

that the tax authority does not observe monopoly profits. The first-order conditions from (7) are:

r, = X a Pit Yi,

kit 9

Restricting our attention to a symmetric equilibrium implies kit = k, , hit = h, , and pi, = p , , for all

i. In this case, (5) and (6) imply that the aggregate production function is

The assumption that the final-goods sector is perfectly competitive implies y, - I,' pi, yi, di = 0.

Substituting yi, =pi:-X y, into this expression and applying symmetry yields pi, = p , = 1. Equations (8a)

and (8b) can then be used to obtain the following expressions for the equilibrium rental rate on capital

and the real wage:


Notice that when xc 1, the rental rate r, is less than the marginal product of capital ay,lk,

implied by equation (9). The after-tax profits in the intermediate-goods sector are given by:

2.3 The Government's Problem

The government chooses an optimal program of taxes, borrowing, and public expenditures to

maximize the discounted utility of the household. To avoid time inconsistency problems, we assume that

the government can commit to a sequence of policies announced at t = 0. Following the approach of

Chari, Christiano, and Kehoe (1994a), we further assume that 7,' and r, are specified exogenously such

that tax revenue collected at t = 0 cannot finance all future expenditures. If the initial levy on private-

sector assets is sufficiently large, then the government chooses zh,= z, = 0 for some t > ;. This case is

not very interesting because after period ;, the model looks identical to one with lump-sum taxes. In per

capita terms, the government's budget constraint in period t is

gl + bl(l+rbt) = bt+, +zhtwrht + rkt[(rt-6)kl + rbrbr] + [ l - ( l - z k t ) ' ] ( l - ~ ) y t ' (I2)

The summation of the household budget constraint (2) and the government budget constraint (12)

yields the following per capita resource constraint for the economy:

Because the resource constraint and the government budget constraint are not independent equations,

equation (13) can be used in place of (12) in formulating the government's problem.

As a condition for equilibrium, government policy must take into account the rational responses

of the private sector, as summarized by (2), (3), (4), (lo), and (1 1). These equations can be conveniently

summarized by the following "implementability constraint":


Equation (14) is obtained by substituting the first-order conditions of the household and the firm

into the present-value household budget constraint.' Since z, and r, are specified exogenously, the

government's problem can be represented as choosing a set of allocations c,, h,, g,, and kt+, , for all t

to maximize household utility (1) subject to (13) and (14), with A,= Uc (c,, h,). Given the optimal

allocations, the appropriate set of prices r, and w, , and policy variables zh, , z,,, and r,, that decentralize

them can be computed using the profit-maximization conditions (lo), the household first-order conditions

(4), and the household budget constraint (2). For example, the optimal allocations define h, and w, from

equations (4a) and (lob). Given h, and w,, (4b) defines the government's optimal choice for z,, .

The government's problem can be written as

subject to

g, = Y, - c, -kt+, + k,( l -S) ,

y, = kta h,'-a , (15)

A, = Uc(c,,h,),

with k,, b,, z,, and r, given. The Lagrange multiplier A associated with (14) is determined

endogenously at t = 0 and is constant over time.

Since the government's problem for t 2 1 is recursive, the solution for t 2 1 can be characterized

o ore specifically, equation (14) is obtained as follows: Multiply both sides of the household budget constraint (2) by A,, substitute in (4a)-(44, (lo), and (1 I), iterate the resulting expression forward and sum over time, and then apply the transversality conditions (4e).


by a set of stationary decision rules for the allocations ct ( s t , A ), h, ( s, , A ), g, ( s, , A ), k,, ( s, , A ),

A,( s, , A ), where s, ={kt , A,-, } . Given these decision rules, a stationary decision rule for the government

bond allocation b,+, ( s f , A ) can be computed as the solution to the following recursive equation:

I - I r Xay, . , Ik , . , -6

~ u h ~ c f + l ~ h ~ + l ~ h f + l ~ ' t + ~ ( ) ( 1 - ~ ) ~ t + 1 + ' 1 + 1 ( k 1 + 2 + b 1 + 2 )

Equation (16) is the household budget constraint at t+l after substituting in the first-order

conditions of the private sector. At t = 0, the government chooses c , , h, , go, k, , and A,. The t = 0

allocations, together with the stationary decision rules for t21, determine A for a given set of initial

conditions.'

3. The Optimal Steady-State Tax on Capital Income

In this section, we derive some expressions to show how the optimal steady-state tax on capital

income zk* depends on the level of profits and the degree to which profits can be taxed. The

government's first-order condition with respect to k,, from (15) is

Omitting time subscripts and dividing by P yields the following steady-state version of equation

(17), where p = 1 / P - 1 is the rate of time preference.

In steady state, the household's first-order condition with respect to kt+, , equation (4c), can be

written as:

2 ~ e e Chari, Christiano, and Kehoe (1994a.b) for more details regarding the solution of the government's problem.

9


When x = 1, profits are zero and (1 8) simplifies to r - 6 - p = 0 (since V, ( g ) > 0). Comparing this

expression to (19) implies z,'=O, which is the result obtained by Judd (1985) and Chamley (1986).

When x < 1, however, there are two competing effects that interact to determine 7,'. First, the rental rate

on capital r which governs household investment decisions is now less than the marginal product of

capital r l ~ . This effect is reflected in the first term of (18) and implies that households underinvest

relative to the socially optimal level. To correct this inefficiency, the government can subsidize capital

accumulation by choosing 7,' < 0. The second term in (1 8) represents an offsetting effect that is driven

by the level of profits and the degree to which profits can be taxed. Since profits do not affect household

decisions at the margin, the government would like to tax profits as much as possible to obtain non-

distortionary revenue. Choosing 7,' > 0 accomplishes this objective in varying degrees, depending on the

value of y. As y increases, the capital tax collects a larger fraction of revenue from profits. As the

quantitative analysis will show, this fact motivates the government to choose a higher capital tax and

a lower labor tax for a given value of X .

Since x appears in both the first and second terms of (18), theoretical conclusions regarding the

sign of 7,' cannot be made except in the special case of x = 1. Depending on the relative importance of

the two effects, the optimal steady-state tax on capital can be positive, negative, or zero. The

underinvestment effect may not be present if profits derive from a different source, such as productive

government expenditures. In this case, Jones, Manuelli, and Rossi (1993) show that the incentive to tax

profits (the profit effect) implies that the optimal steady-state tax on capital is positive.

4. Computation Procedure

Given the inconclusive nature of the theory, we now turn to a quantitative assessment of the

optimal capital tax in a calibrated version of our model. The steady-state allocations implied by (15)

depend on parameter values (which are described below) and the endogenous Lagrange multiplier A,

which is computed as follows. First, given an initial guess for A, we compute the steady-state allocations

c, h, g, k, and h from the first-order conditions of (15) with respect to c,, h,, g,, k,, , and 1 , . We then


use the steady-state version of (15) to compute the steady-state level of government debt b. We repeat

this procedure, adjusting A until we obtain a desired ratio of steady-state debt to output. The initial level

of debt b, that is consistent with A and b can be computed using the first-order conditions of (15) with

respect to c, , h, , go, k, , and h, , together with the stationary decision rules for t 2 1, the household

budget constraint (2) evaluated at t = 0 and t = 1, and the initial conditions k, , z, , and r, .

Once the optimal steady-state allocations are known, we use (lOa), (lob), (4b), and (4c) to

determine the optimal steady-state tax policy {z; , 7; } that decentralizes the allocations. This procedure

is repeated over a range of values for x and y. In each case, we compute the welfare loss from

switching to a "naive" policy that sets z, = 0 and adjusts z, to achieve the same levels of g and b as the

optimal policy. We also compute the welfare gain of switching from the existing U.S. tax policy to an

optimal policy, again holding the levels of g and b ~ons tan t .~ We use the steady-state level of the

household's within-period utility function as our basic welfare measure. This facilitates a simple

comparison between our results and those of Lucas (1990) and Cooley and Hansen (1992), who consider

the welfare effects of capital taxation in models with zero profits. Since a time period in the model is

taken to be one year (consistent with the frequency of most government fiscal decisions), the change in

steady-state utility across policies can be readily translated into an annual gain or loss and expressed as

percentage of total output.

A more comprehensive welfare analysis would obviously need to take into account the dynamic

transition between steady states. However, during the first period of the transition, the government in

our model has a strong incentive to impose a heavy tax on the existing stock of household assets in

order to minimize distortions. Chari, Christiano, and Kehoe (1994a) show that the welfare gains from

this initial levy tend to dominate any differences between final steady state^.^ Although this scenario

provides an interesting motivation for tax reform, it is doubtful that confiscatory taxes of this kind are

3 ~ n particular, we follow the approach of Lucas (1990) and assume that the net change in debt is zero along the transition path between steady states. This implies that tax rates along the transition path are set such that the implementability constraint is satisfied. Alternatively, we could assume that lump-sum taxes are available during the first period of the transition to satisfy the implementability constraint. See Chari, Christiano, and Kehoe (1994b) for a more detailed discussion of this point.

k v e n though 7, is specified exogenously, z,, tends to be much higher than the optimal steady-state value z,'. In addition, the large positive value of z,, typically implies z,,, c 0.


politically feasible. Lucas (1990), Cooley and Hansen (1992), and Mendoza and Tesar (1995) adopt an

alternative approach to transitional dynamics by assuming that shifts in tax rates between steady states

are exogenous. They obtain a quite different result--that transitions involve a welfare loss. This loss

reduces the available gains from moving to a more desirable steady state. Given the many ways in which

transitions can be modeled, we have chosen to abstract from these issues and report results only from

steady-state welfare analysis. Our results must therefore be qualified to the extent that transitions

between steady states produce significant benefits or costs.

5. Calibration

Parameters are assigned values based on empirically observed features of postwar U.S. data. The

discount factor p (= 0.962) implies a real rate of interest of 4 percent. The household's within-period

utility function is specified as

where the linearity in hours worked draws on the formulation of indivisible labor described by Rogerson

(1988) and Hansen (1985). This means that all fluctuations in total labor hours are due to changes in

the number of workers employed, as opposed to variations in hours per worker.' The parameter A

(= 2.48) is chosen such that the fraction of time spent working is approximately equal to 0.3. The value

of B (= 0.346) is chosen to yield a steady-state ratio g l y close to 0.22. The private capital depreciation

rate 6 (=0.067) is estimated by a least-squares regression of x, - (k,, - k,) on kt .6 The Lagrange

multiplier A is set to achieve a steady-state ratio b l y =0.37 under the optimal policy. This is the

average level of U.S. federal debt held by the public as a fraction of GNP from 1954 to 1992. The

steady-state values of g and b under the optimal policy are then used as exogenous inputs to compute

the steady-state allocations under the z, = 0 policy.

' ~ n postwar U.S. data, about two-thirds of the variance in total hours is due to changes in the number of workers. See Kydland and Prescott (1990).

%e capital and investment series are in 1987 dollars from Fixed Reproducible Tangible Wealth in the United States, U.S. Department of Commerce (1993). The series for k, and x, include business equipment and structures, consumer durables, and residential components. The "capital input" measure of the net stock was used for all capital data.


To compute the welfare gain of switching from the existing U.S. tax policy to an optimal policy,

we follow Cooley and Hansen (1992) and take U.S tax policy to be z, = 0.50 and z, = 0.23. The steady-

state level of government debt under the U.S. policy is specified exogenously such that b / y = 0.37. We

then determine the steady-state value of g as a residual such that the government budget constraint (12)

is satisfied. To compute 7,' and 7,' under the revenue-neutral optimal policy, we adjust the Lagrange

multiplier A to achieve the same level of steady-state debt as the U.S policy and treat the required level

of government spending g as an exogenous constraint.'

We examine a range of values for the parameter X, which determines the steady-state ratio of

monopoly profits to output. The profit ratio s, is linked to the markup of price over marginal cost

according to the formula

where v represents the degree of returns to scale in the intermediate-goods sector. Our use of a constant-

returns-to-scale specification in (6) implies v = 1 and s,= 1-X. Using data on U.S. manufacturing

industries over the period 1953-1985, Basu and Femald (1994a) obtain a point estimate of v = 1.03, but

this is not statistically different from 1. Basu and Fernald (1994b) find that the typical manufacturing

industry has an average profit ratio of about 0.05. Based on these results, we choose x =0.95 as our

baseline value, which implies p / mc = 1.05. In the computations, we examine profits ratios over the range

0 to 0.13.

The shares of total output received by capital and labor in the model are X a and ~ ( 1 - a ) ,

respectively. Given the baseline value of X, we set a = 0.34 such that capital's share is 0.32 and labor's

share is 0.63. These values lie within the ranges estimated by Christian0 (1988) for the postwar U.S.

economy. Finally, since dividends are subject to double taxation under the U.S. tax code, we choose

y = 2 as our baseline.

7 The government's first-order conditions from (1'5) must be modified slightly for this experiment to allow for the fact that g, under the optimal policy is no longer endogenous. This can be done very simply by replacing the marginal utility of public consumption V, (g,) with &, where & is the Lagrange multiplier associated with the resource constraint (13).


6. Quantitative Results

Table 1 and figures 1-3 show the optimal steady-state tax rates over a range of profit ratios and

degrees of dividend taxation. When 1-x = 0, figures 1-3 each indicate that 7,' = 0, consistent with the

results of Judd (1985) and Chamley (1986). Figure 1 shows that when dividends are not taxed (y= 0),

2,' becomes increasingly negative as the profit ratio rises. In this case, the underinvestment effect from

the first term in equation (18) dominates the profit effect associated with the second term. At the

baseline profit ratio, the model implies 2,' = -0.057 (see table 1). When y equals 1 or 2, however, the

profit effect dominates and 7,' becomes increasingly positive as the profit ratio rises (figures 2 and 3).

Moreover, table 1 shows that higher values of y cause 7,' to increase relative to 7 ; . As noted earlier,

a higher y implies that the capital tax collects a larger fraction of revenue from profits. Since profits do

not distort household decisions, this calls for a higher capital tax, thereby allowing the distortionary tax

on labor to be reduced.

At the baseline values of 1-x = 0.05 and y = 2, table 1 indicates that the optimal tax policy is

2,' = 0.236 and 7,' = 0.279. It is interesting to compare these values to some tax rate estimates for the

U.S. economy. Jorgenson and Sullivan (1'981) estimate an average effective corporate tax rate of 0.30

for the period 1947-1980. Barro and Sahasakul (1986) estimate an average marginal tax rate on labor

income of 0.27 for the period 1947-1983. Sample average estimates by McGrattan, Rogerson, and

Wright (1993) are zk = 0.57 and zh = 0.23 for the period 1947-87, while Mendoza, Razin, and Tesar

(1994) estimate zk = 0.43 and zh = 0.25 over the period 1965-1988. In general, the U.S. tax rate on

capital income appears to be higher than the optimal value of 7,' = 0.236 implied by our baseline model.

However, we note that our model abstracts from some important considerations which, if taken into

account, could increase the optimal tax rate on capital to a value which is closer to U.S. estimates. Jones,

Manuelli and Rossi (1993) show that rents associated with productive public goods can give rise to a

positive optimal tax rate on capital in the long run. In models without profits, Aiyagari (1994) and

~mrohoroglu (1994) show that a positive optimal tax rate can also be obtained by introducing borrowing

constraints and idiosyncratic income shocks among heterogeneous agents.

Figure 4 plots the welfare cost of switching to a naive policy that sets zk = 0 and maintains g

and b at the levels implied by the optimal policy. The welfare cost increases rapidly as a function of


profits when y= 2, but stays very close to zero when y= 0. This shows that the structure of dividend

taxation can have dramatic effects on household welfare. This is not surprising, since changes in y affect

the government's ability to obtain nondistortionary revenue by means of a tax on profits.' Starting from

the baseline optimal policy, the welfare cost of eliminating the capital tax is about 1.6 percent of total

output (see table 1). This figure translates to an annual loss of $407 per person in 1994.'

In models without profits, Lucas (1990), Cooley and Hansen (1992), and McGrattan, Rogerson,

and Wright (1993) all estimate large available gains from eliminating the U.S. capital income tax.

Excluding transitional dynamics, Lucas reports that steady-state consumption increases by 4.2 percent,

while McGrattan, Rogerson, and Wright report an increase of 9 percent. Cooley and Hansen report a

welfare gain of 7.8 percent of steady-state o~ tpu t . '~ Table 2 computes the available welfare gains of

switching from the existing U.S. tax policy to an optimal policy, holding revenue constant. The

requirement to maintain revenue neutrality pushes up the optimal tax rates in comparison to the values

reported earlier in table 1.

In table 2, the available gains depend crucially on the value of y. When y= 0, the gains are

large, equal to 3.88 percent of steady-state output. In this case, the U.S. policy of z, = 0.50 is very far

from the optimal policy of 7,' = 0.016. When y equals 1 or 2, however, the available welfare gains are

less than 1 percent of steady-state output. The gains are much lower in these two cases because revenue

that was previously obtained by a tax on profits must now be replaced with a higher tax on labor. If tax

rates are considered to be exogenous during the transition between steady states, then these welfare gains

are likely to be even lower, and could even turn into welfare losses. This experiment shows that previous

claims regarding the benefits of reducing the U.S. capital tax may be overstated.

'see Guo and Lansing (1995) for a more comprehensive analysis of the effects of tax structure on household welfare.

his number is based on a nominal GNP of $6,729 billion and total U.S. population of 260.7 million in 1994.

''TO compute these gains, Lucas uses a value of 0.36 for the U.S. tax rate on capital income, while McGrattan, Rogerson, and Wright use 0.57, and Cooley and Hansen use 0.50.


7. Concluding Remarks

This paper has shown that the introduction of monopoly power in an otherwise standard

neoclassical growth model creates a theoretical ambiguity regarding the sign of the optimal steady-state

tax on capital income. The optimal tax rate in the long run can be positive, negative, or zero, depending

on the relative strength of two competing forces, which we label as the underinvestment effect and the

profit effect. In particular, the underinvestment effect supports the use of a negative tax rate on capital

income to induce monopolistic firms to produce the socially optimal level of output. The profit effect

supports the use of a positive tax rate on capital income to minimize distortions in the financing of

government spending.

In the quantitative section of the paper, we found that empirically plausible values for the

model's parameters imply that the profit effect dominates such that the optimal tax rate is positive. In

applying our model to the important policy question of whether or not the U.S. capital tax should be

reduced, we found that the welfare gains from such a policy can be large or small, depending on the

structure of dividend taxation.


REFERENCES

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Table 1: Optimal Steady-State Tax Rates and Welfare Comparison with z, = 0 Policy

Profit Ratio = 1-x = 0.05 I Profit Ratio = 1-x = 0.10

Labor tax with 2, = 0

Variable y = O y = 1 y = 2

2,' -0.057 0.188 0.236

7; 0.346 0.301 0.279

y = O y = 1 y = 2

-0.088 0.293 0.315

0.357 0.267 0.232

a ~ h e welfare loss is defined as AUl(hy), where AU is the change in steady-state utility and h and y are the steady-state values associated with the optimal policy.

Welfare loss 0.079 % 0.500 % 1.576 %

from 2, = 0 policya

Source: Authors' calculations.

0.059 % 3.452 % 7.731 %

Table 2: Available Welfare Gains from Reducing U.S. Capital Tax

Profit Ratio = 1-x = 0.05

Variable y = O y = 1 y = 2

2,' (new policy)

2,' (new policy)

Welfare change from U.S. policy of

2, = 0.50 and 2, = 0.23a

a ~ h e welfare change is defined as AUl(hy ), where AU = U,,, - U,, and h and y are the steady-state values associated with the U.S. policy.

Source: Authors' calculations.


Fig 1 : TAX RATES vs PROFIT RATIO Ze ro Tax o n Div idends y=O

Fig 2 : TAX RATES vs PROFIT RATIO Sing le Tax a n Div idends y = l

0.60

0.55

0.50

, 0.45

' 0.40

*= 0.35 k-

0.30 .I

0.25

bl 0.20 a, .+ 0.1 5

0 . 1 0 - X 0 0.05 +

-0.00

-0.05

-0.10

- O . ' ~ . O O

7 h - Labor Tax with rk=O pal icy _ _ - - - _ _ - - -

_ _ _ - - - - - x

" " - " ,-, - 0

I 0.02 0.04 0.06 0.08 0.10 0.12 0.14

P r o f i t R a t i o n/y = 1 -X


- -

-

F ig 3: TAX RATES v s PROFIT RATIO Doub le Tax a n Div idends y=2

+ 7; - Optimal Copitol Tax e 7.h - Optimal Lobar Tax - - r h - Labor Tax with rk=O Policy

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14


-

n n n ,-, n ,, ;

" " " " 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -

'

-

-

-

' -

" - X

0.02 0.04 0.06 0.08 0.10 0.12 0.14

SOURCE: Authors' calculations.


Welfare Lass f rom T,=O Policy w i t h 7=2 Welfare Lass f rom rk=O Policy with 7=1 Welfare Lass f rom T~=O Policy with 7=O

/ /

y = l / I

/

y = 0 -

Fig 4: WELFARE LOSS FROM 7, = 0 POLICY

30 n

X X V

\ 3 26 4

SOURCE: Authors' calculations.

0 0 -

1 1 22 n +- 3 a 5 18 0 * 0

5 14 (0 (0

0 J

10 0 r

; W E +- 0 +- m

2 2 w +- m

-2 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Pro f i t Ratio n/y = 1 -X


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